Relations
Scope of Relations in JEE :- Sets and Relations comes together in JEE mains and its not included in JEE Advanced syllabus. but its a fundamental topic to start with the preparation of JEE.
What is Relations(Briefly Described)?
This topic “Relations and Functions” is a foundation or fundamental of algebra in mathematics. Relations and functions are two different words having different meaning mathematically. Many us you might be confused in their difference. We shall study both these concepts in detail here.
Same as the relations which we have in our daily life, a kind of relations also exists in algebra.
In daily life, relations are like brother and sister, friends, student and teacher and many more. In mathematics also we see some relations like a line is parallel or perpendicular to another, any one variable is greater or less than the another variable. Any Set A is subset of B, all these are examples of relations.
One thing which we see in common while studying relations, that it required two different objects to link two different objects via relations.
For Example
Consider a set A containing elements as {1, 2, 3} and set B contains elements as {2, 4, 6}.
Then the relation between Set A and B from A to B will be set of any combinations from Set A to set B.
From the above diagram, we can see that Relation from A to B i.e. R will be set of {(1,4). (1,2), (3,4), (3,2)}. This relation is a subset of the Cartesian product of two sets A X B.
Let’s take another example where, set A = {1, 2, 3} and set B = {1, 2, 3, 4, 5, 6, 7, 8, 9}.
If the Relation between A and B is as: elements of B is the squares of elements of set A, then the relation is written in the form of sets as:
R = {(a,b): where b is square of a and a ∈ A & b ∈ B}
Then R = {(1,1), (2,4), (3,9)}
Same as sets, relation may also be represented algebraically either by the Roster method or by the Set-builder method.
Relation can also be defined as a linear operation which establishes relationship between the element’s of two set’s according to some definite rule of relationship.
For complete information:-I m providing the link to my notes which are more than sufficient for JEE mains as well as for Boards :- Relations
KL Rahul scored a scintillating 101 off 54 balls powering India to an 8-wicket win against England in the first T20I at Old Trafford on Wednesday. Scoring his second T20I hundred, Rahul whacked the English bowlers all over the park hitting 10 boundaries and 5 sixes. Chasing a target of 160 on a batting surface, India lost Shikhar Dhawan early. Rahul came in to bat at number three position and was middling the ball from the word go. Rahul clobbered all England bowlers to every corner of theground. Rohit Sharma (32 off 30 balls) provided brilliant support from the other end. No England bowler seemed troubling the batting duo. Adil Rashid was the most successful picking 1 wicket for 25 runs. Virat Kohli also became the fastest batsman to reach 2000 runs in T20I format in the match. At the end India achieved the target with 10 balls to spare.
“The Union Cabinet chaired by Prime Minister Shri Narendra
Modi has approved the creation of a National Testing Agency (NTA) as a Society
registered under the Indian Society Registration Act, 1860, and as an
autonomous and self-sustained premier testing organization to conduct entrance
examinations for higher educational institutions,” said a press release.
Fans of Cricket can buy this legendary bat made of Kashmir willow at an affordable cost via the given link :-MC special edition spartan Bat
